Dynamic Paint texture with Cycles
To get the frames to update when previewing in the 3D viewport, you need to enable Auto Refresh on the image texture. In final render, this is not needed.



This is not documented in the online manual's section on the Image Texture node, and the only references I've found to it are on the various help sites for Blender. Therefore I can't say for sure why this is so, but I'm assuming that in the 3D viewport speed is given priority over accuracy, while renders give priority to accuracy over speed.

In this answer to a related question, it is mentioned by Ray Mairlot. I've seen this mentioned in other places as well, but this was the first one a quick search turned up.

You may also want to try using the Alpha socket of the image texture as input for the Fac socket of the mix node, though that will depend on how the dynamic paint was set up.